This discussion isn't going in the direction I was hoping for, ha ha!

But as a developer of these sites I've used the majority to check my own domains and the most reliable one I've found is https://www.ipqualityscore.com/

I strongly recommend that you take another look at your signup process though and don't require users to give up their email addresses, instead make it optional and present an alternative like a captcha.

I've never evaluated any myself, but became acutely aware of them after launching my own temporary mail service as a learning exercise. I think there's a github repo somewhere that's regularly updated with a block list of these cycled domains though.

verifymail.io is a pretty decent source, though I don't know what they charge for API access.